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(II) A person of mass 75 $\mathrm{kg}$ stands at the center of a rotatingmerry-go-round platform of radius 3.0 $\mathrm{m}$ and moment of inertia920 $\mathrm{kg} \cdot \mathrm{m}^{2} .$ The platform rotates without friction with angularvelocity 0.95 $\mathrm{rad} / \mathrm{s}$ . The person walks radially to the edge of the platform. (a) Calculate the angular velocity when the person reaches the cdge. (b) Calculate the rotational kineticenergy of the system of platform plus person before and after the person's walk.

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a) 0.55 $\mathrm{rad} / \mathrm{s}$b) 240$J$

Physics 101 Mechanics

Chapter 11

Angular Momentum; General Rotation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

University of Sheffield

University of Winnipeg

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

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A person of mass $75 \math…

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(II) A person of mass 75 k…

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(II) A person of mass 75 $…

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A circular platform is mou…

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A man stands on a rotating…

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(II) A person stands on a …

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A man stands on a friction…

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(II) A woman of mass $m$ s…

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A horizontal platform in t…

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A 70 -kg person stands on …

party, we can apply the conservation of angular momentum. And we can then say that the moment of inertia for the platform multiplied by the initial angular velocity would be equaling the moment of inertia of the platform, plus the moment of inertia of the person multiplied by the final angular velocity. And so the final angular velocity would be equaling the moment of inertia of the platform divided by the moment of inertia for the platform, plus the moment of inertia for the person. And we can then say that the moment of inertia of the person is simply gonna be m r squared so we can replace the moment of inertia of the person. And this would be M R squared times the initial angular velocity and this would be equally 920 kilogram meters squared, divided by 920 kilogram meters squared plus 75 kilograms times 3.0 meters, quantity squared, multiplied by 0.95 radiance per second. And we find that the final angular velocity it is gonna be equaling 0.548 radiance per second. This would be our answer for part A for part B. Now we're going to say that the initial kinetic energy would be equaling the rather 1/2 times the moment of inertia for the platform multiplied by the initial angular velocity squared. This is equaling 1/2 times 920 kilogram meters squared, multiplied by 0.95 radiance per second on then, quantity squared. This is gonna be equaling. Essentially 420 Jules, approximately. And so we can stand say that the final kinetic energy would be equal in 1/2 times the moment of inertia of the platform rather plus the moment of inertia of the person which would be the mass of the person times R squared, multiplied by the final angular velocity. And so we can then say that the final kinetic energy would be equal in 1/2 multiplied by 920 plus 75 kilograms times 3.0 meters quantity squared. Of course, the units here would be kilograms meters squared, multiplied by our answer to part a 0.548 radiance per second quantity squared. This is equaling approximately 240 Jules rounded to two significant figures. So this is our final kinetic energy and our initial kinetic energy. That is the end of the solution. Thank you for watching

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